To prove our lower bounds
we use the known framework of reductions from 2-party communication problems or reduce to lower bounds that have been proven with this framework. This framework was pioneered by Peleg and Rubinovich [1]}, and has been used extensively since then to obtain lower bounds for bandwidth restricted models (see, e.g., [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}).
The novelty in our proofs lies in the constructions of the graph families that give our reductions. We first recall the framework itself, as follows.
